Connected components of special cycles on Shimura varieties
Number Theory
2025-05-06 v1 Algebraic Geometry
Abstract
I use methods of Chai-Hida and ordinary -Hecke correspondences to study the set of irreducible components of special fibers of special cycles of sufficiently low codimension in integral models of GSpin Shimura varieties, and apply this to prove irreducibility results for the special fibers of the moduli of polarized K3 surfaces. These results are also applied in joint work with Howard on the modularity of generating series of higher codimension cycles on GSpin Shimura varieties.
Keywords
Cite
@article{arxiv.2505.02084,
title = {Connected components of special cycles on Shimura varieties},
author = {Keerthi Madapusi},
journal= {arXiv preprint arXiv:2505.02084},
year = {2025}
}
Comments
Updated version of an old article 'On the irreducibility of the moduli of K3 surfaces in finite characteristic' which is still on my website